University of Groningen Enrichment of planetary surfaces by asteroid and comet impacts Frantseva, Kateryna

Enrichment of planetary surfaces by asteroid and comet impacts

Frantseva, Kateryna

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10.33612/diss.100695383

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Frantseva, K. (2019). Enrichment of planetary surfaces by asteroid and comet impacts. Rijksuniversiteit Groningen. https://doi.org/10.33612/diss.100695383

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5. E

NRICHMENT OF THE

HR 8799

PLANETS BY ASTEROIDS

AND COMETS

Kateryna Frantseva, Michael Mueller, Floris F.S. van der Tak, Inge Loes ten Kate Submitted to Astronomy & Astrophysics

H

• The exoplanetary system HR 8799 is know to harbour two debris belts and four giant planets in between the belts.

• The minor bodies from the inner and the outer belts deliver volatile and refractory materials to the fours giant planets.

• The amount of delivered volatiles and refractories may be observable. • A potential detection of refractory material in the planets’

A

Context. In the Solar System, asteroids and comets deliver various materials to planetary surfaces. Several exoplanetary systems are known to host inner and outer belts, analogues of respectively the Main Asteroid Belt and the Kuiper Belt.

Aims. We study the possibility that exoasteroids and exocomets deliver volatiles and refractories to the exoplanets in the well-characterised system HR 8799. Methods. We use the MERCURIUS integrator (REBOUND software package) to perform N-body simulations to study the impact rates of asteroids and comets in the system HR 8799. The model consists of the host star, 4 giant planets (HR 8799 e, d, c and b), 650,000 test particles representing the inner belt and 1,450,000 test particles representing the outer belt. The simulations are performed over the estimated age of the system, 70 Myr.

Results. Within a Myr, the two belts evolve toward the expected dynamical structure (also derived in other works), where mean-motion resonances with the planets carve the analogues of Kirkwood gaps. We find that, after this point, the planets suffer impacts by objects from the inner and outer belt at rates that are essentially constant with time. We convert these to volatile and refractory delivery rates using our best estimates of the total mass contained in the belts and their volatile/refractory content. Over their lifetime, the four giant planets receive between 10´4_{and 10}´3_M

Cof material from both belts.

Conclusions. The amount of delivered volatiles and refractories, 4 ˆ 10´3_M C,

is small compared to the total mass of the planets, 11 ˆ 103_M

C, but may

be observable. If terrestrial planets exist within the snow line of the system volatile delivery would be an important astrobiological mechanism and may be observable as atmospheric trace gases.

5.1. INTRODUCTION

5.1

I

The first exoplanet discovery (Mayor & Queloz, 1995) around a main-sequence star has started a new chapter in the field of planetary sciences. More than 4,000 confirmed exoplanets have been detected as of September 2019 and the number doubles every „27 months1_{. The variety of the}

discovered exoplanets shows that planetary systems are very common (planets are probably as common as stars) and diverse (Perryman, 2018). There are exoplanets with masses ranging from the Moon’s mass to hundreds of Jupiter masses, with orbital periods ranging from hours to thousands of years and with a great variety in mass densities from that of H2gas to that of solid iron (Winn & Fabrycky, 2015). A large fraction

of the discovered exoplanets do not have analogues in the Solar System, for example super-Earths, with masses between about 1 and 10 Earth masses, and hot Jupiters, giant planets orbiting very close to their host stars (Raymond et al., 2018). Importantly, though, there appears to be a population of terrestrial planets at distances to the star that may allow liquid water to exist on the surface, possibly allowing life as we know it to form.

Figure 5.1: Orbital structure of the Solar System, left, and the HR 8799 system, right. The inner belts are represented in red and the outer belts in blue. Planet masses are indicated by the size of the dots; each plot has a separate log scale. Note that orbital eccentricities of the giant planets in the HR 8799 system is few times larger than eccentricities of the Solar System giants, which will lead to more impacts between planets and small bodies.

Apart from looking for analogues of the Solar System planets, a search for analogues of small body populations is ongoing. Recent observations (Acke et al., 2012; Booth et al., 2016; Close, 2010; Lagrange et al., 2010; Matthews et al., 2014; Mo´or et al., 2013; Su et al., 2013; Welsh & Montgomery, 2013) found analogues of the Main Asteroid Belt (MAB) and the Kuiper Belt (KB) around „20% of the nearest stars (Ren et al., 2019). Within our own Solar System the small body belts (MAB and KB) play an important role in delivering volatiles to planets (e.g. Frantseva et al., 2018, 2019). For example, the atmospheres of the terrestrial planets have originated from delivery processes (besides outgassing, de Pater & Lissauer, 2015). In the MAB certain types of asteroids, C-types, together with comets and small bodies from the KB are known to contain significant amounts of water and organic compounds. Migration of these small bodies occasionally results in impacts with planets, which in turn leads to volatile enrichment of the planets. The existence of asteroid belts in other planetary systems implies that the same volatile delivery mechanisms might be at play around other stars. This way, volatile material, in particular water and organic compounds, can be delivered to exoplanets. Studying these delivery mechanisms is of astrobiological interest and will lead to better understanding of planetary formation, evolution, and habitability (Raymond et al., 2018). Enrichment of exoplanet atmospheres in refractory materials is of less astrobiological relevance, but may become observable using JWST-MIRI, due to be launched in 2021. Silicate features, in particular, feature prominently in MIRI’s wavelength range (see, e.g., Rieke et al., 2015). The atmospheres of exoplanets beyond the snow line would not be expected to contain significant amounts of refractory materials, so any detection thereof would be diagnostic of impact-driven enrichment.

In this paper we focus on the exoplanetary system HR 8799, which is known to host both a warm and a cold debris belt, which are analogues of the Main Asteroid Belt and the Kuiper Belt. Modelling such a planetary system helps in understanding the interaction between planets and planetary debris.

HR 8799 is a nearby young A5V star with mass « 1.5Md(Gray & Kaye,

1999; Gray et al., 2003; Baines et al., 2012; Go´zdziewski & Migaszewski, 2014). The exact age of the star is somewhat uncertain between 30 and 60 Myr (Marois et al., 2010; Zuckerman et al., 2011). HR 8799 is the host star of four giant planets HR 8799 e, HR 8799 d, HR 8799 c, and HR 8799 b detected via direct imaging (Marois et al., 2008, 2010). HR 8799 e, HR 8799 d and HR 8799 c have masses of approximately 9M_jup, and HR 8799 b of 7M_jup. For comparison, the giant planets in the Solar System have masses of 1Mjup, 0.3Mjup, 0.05Mjup and 0.04Mjup, see

5.1. INTRODUCTION

Figure 5.1. HR 8799 e, HR 8799 d, HR 8799 c and HR 8799 b orbit their host star at distances of 15 - 64 AU, see Table 5.1 for more details. The Solar System giant planets orbit closer to the host star at 5.2 AU, 9.5 AU, 19.2 AU and 30.1 AU.

The orbits of the HR 8799 planets are not well characterised observa-tionally, yet. The available astrometry spans only » 12% of the innermost planet’s orbit and » 3% of the outermost planet’s. A variety of orbital configurations are consistent with the data, most of which are dynamically unstable; however, a few stable configurations were found (Go´zdziewski & Migaszewski, 2014; G¨otberg et al., 2016; Go´zdziewski & Migaszewski, 2018; Wang et al., 2018). The best long-term stable solution assumes that the four planets are locked in a protective mean motion resonance 1:2:4:8 (Go´zdziewski & Migaszewski, 2014, 2018). The higher planetary masses relative to the star as well as the larger eccentricities make planet-planet interactions more important in HR 8799 relative to the Solar System. This leads to many unstable orbital configurations consistent with the data (see above), and also requires extra care in numerical modelling. A good understanding of the orbital architecture of the system is essential for studying the system’s debris belts that have been observed with the Herschel Space Observatory, the Atacama Large Millimeter/submillimeter Array (ALMA) and the Spitzer Space Telescope (Su et al., 2009; Su & Rieke, 2014; Matthews et al., 2014; Booth et al., 2016).

The system contains at least two distinct debris belts: an inner belt and an outer belt. The outer belt was discovered in Spitzer-MIPS imaging and is spatially resolved, while the inner belt is too small to be spatially resolved, but was inferred from the observed IR excess in the SED using Spitzer-IRS data (Su et al., 2009). The inner belt lies between „6 AU and „15 AU, and the outer belt extends from „90 AU to „310 AU. The inner belt lower dust mass limit was estimated to be 1.1 ˆ 10´6_M

C and

the outer belt’s is 0.12MC(Su et al., 2009). These estimated belt masses

are dust-only masses, but large objects (if they exist) will by far dominate the mass budget. The structure of HR 8799 resembles the structure of our own Solar System on a larger scale as shown in Fig. 5.1. The Solar System up to the Kuiper belt can be fitted inside the orbit of the outermost planet of the HR 8799 system. Both systems contain an inner warm belt close to the host star, within „6 AU and „15 AU for HR 8799 and within „2 AU and „4 AU for the Solar System. Furthermore, both systems contain an outer cold belt, within „90 AU to „310 AU for HR 8799 and „35 AU to „100 AU for the Solar System. Between the two belts each of the systems have four giant planets. Remarkably, HR8799 and the Solar System show the same overall structure although the HR8799 system is much larger

than the Solar System and its planets are much more massive (see Fig. 5.1). Note that terrestrial planets may exist inside the warm belt of HR8799; those would not be detectable using current telescopes.

The interaction between the giant planets of HR 8799 and the debris belts have been studied by Contro et al. (2015, 2016); Read et al. (2018); Go´zdziewski & Migaszewski (2018). Numerical simulations by Contro et al. (2016) indicate that the inner belt is structured, with gaps at the locations of mean motion resonances with the innermost planet similar to the Kirkwood gaps in the MAB. Moreover, the belt is located between 6 AU and 8 AU and collisions within the belt occur at velocities of the order of 1.2 km/s or less, lower than the collisional velocities in the MAB, which are of order 5 km/s. Note that Contro et al. place the outer edge of the inner belt at 8 AU, and not 15 AU as suggested by past observations by Spitzer. Due to the chaotic region of the innermost planet it is not possible to keep a population of small bodies between 8 and 15 AU. Similarly, Read et al. (2018) performed N-body simulations to study the effect of the giant planets on the outer belt and demonstrated that the belt has a similar structure as the inner belt, with gaps at the locations of the mean motion resonances with the outermost planet. Read et al. (2018) showed that adding a hypothetical planet with mass 0.1 ´ 1 Mjupoutside HR 8799 b,

the outermost confirmed planet, will push the belt outwards, providing a better fit to ALMA observations (Booth et al., 2016; Read et al., 2018).

In our own Solar System the interaction between the belts and the planets leads to scattering of small bodies within the system and beyond. Sometimes this scattering leads to impacts with the planets. For the terrestrial planets impacts can appreciably enrich the surface in numerous materials including volatiles. For the giant planets refractory enrichment is even observable, as in the case of the Shoemaker-Levy 9 impacts in 1994 (Atreya et al., 1999; Harrington et al., 2004; Fletcher et al., 2010). Here, we test for the first time how strong this effect is in the HR 8799 system. We perform several sets of dynamical N-body simulations with 1,600,000 test particles representing exoasteroids and exocomets. These simulations result in impact rates with the giant planets which are then converted to volatile delivery rates.

In Section 5.2 we describe our N-body simulations. Section 5.3 presents the results of the numerical simulations, checks for consistency with previous results, and determines impact rates. In Section 5.4 we convert the latter to volatile delivery rates to the planets. Our findings and conclusions are presented in Sections 5.5 and 5.6.

5.2. NUMERICAL SIMULATIONS

5.2

N

We have performed numerical simulations of the dynamical evolution of the inner and outer belts in the exoplanetary system HR 8799 to study the volatile and refractory influx onto the four known giant exoplanets. We used the N -body integrator MERCURIUS (Rein et al., 2019) from the software package REBOUND (Rein & Liu, 2012). We set up a model of the motion of one gravitationally dominant object (HR 8799) and N massive objects (in our case: N “ 4 representing the four planets in the system) under the influence of their mutual gravity over Myr timescales forward in time. Simulations focusing on the inner and outer belts are done separately, as described below. The inner belt is represented by 650,000 test particles and the outer belt by 1,450,000. Our first run of the outer belt simulation contained 650,000 test particles and one of the planets received 0 impacts. Therefore, in order to overcome small number statistics we added more test particles to the outer belt simulation. The test particles move passively under the influence of the combined gravitational potential of the star and the planets. The gravitational effect of the test particles on one another and on the massive objects is neglected.

Test particles are removed from the simulation once they collide with a planet or with the star. Moreover, test particles are considered ejected from the planetary system and discarded when they exceed a user-provided heliocentric distance: 1,000 AU for the inner-belt simulations and 10,000 AU for the outer-belt simulations following Contro et al. (2016) and Read et al. (2018), respectively. Time step values were set separately for the inner and outer belts, see Subsection 5.2.1 and Subsection 5.2.2 for a detailed description. The simulation results are recorded by taking snapshots of the simulations at predefined times (6 Myr, 30 Myr, 60 Myr and 70 Myr).

Table 5.1 presents the planetary initial conditions that have been adopted for our simulations. The masses and orbital parameters were taken from Go´zdziewski & Migaszewski (2014, their Table 1). Inclination, i, of the four planets is the best-fitting inclination of coplanar orbits to the sky plane, while the inclination of the HR 8799 equator to the sky plane is „ 23 deg as following form the statistical analysis of the rotational speed of A5 stars. For the longitude of the ascending node, Ω, Go´zdziewski & Migaszewski (2014) assumed the same value for all four planets. The planetary radii (0.0005327 AU, 0.0005327 AU, 0.0005327 AU and 0.000538629 AU) were

calculated using the ”Jovian Worlds” mass-to-radius relation from Chen & Kipping (2017): R RC “ 17.74ˆ M MC ˙´0.044 , (5.1)

which is valid for 0.414 Mjup ă M ă 83.79 Mjup. The relation

represents population of planets with masses larger than a sufficient mass for gravitational self-compression which starts reversing the growth of the planet (therefore the exponent is negative). Radii are needed to model impacts: a test particle is considered to have impacted the star or a planet once it ventures within its radius. For the radius of the star, we adopt a value of 1.440 ˘ 0.006 Rd(Baines et al., 2012) and 60 Myr for its age

(Marois et al., 2010).

5.2.1 Inner belt

To model the inner belt of the HR8799 we followed the initial conditions described in Contro et al. (2016). We used 650,000 test particles (500,000 in Contro et al. (2016)) with semi-major axes between 1 and 10 AU. We adopt 1 AU as the inner edge value of the simulations following Contro et al. (2016). The outer boundary, 10 AU, follows the estimated observational value as in Marois et al. (2010). The eccentricities of the particles are distributed uniformly between 0 and 0.1 and the inclinations are set between 0˝ _{and 5}˝_{. The remaining, angular, orbital elements are set to}

random numbers between 0˝ _{and 360}˝_{. The simulations were performed}

for 70 Myr forward in time. The time step of the simulations is set to 7 days in order to resolve the orbits of the innermost test particles orbiting the star at 1 AU with an orbital period of 292 days.

5.2.2 Outer belt

The outer belt simulations were based on the initial conditions from Read et al. (2018). We created 1,450,000 test particles (50,000 in Read et al. (2018)) with semi-major axes between 69.1 and 429 AU. The inner boundary of the disk is set to the semi-major axis of the outermost planet HR 8799 b. Note that ALMA observations (Booth et al., 2016) suggest that the inner edge of the disk has to be further out at 145 AU, which might be explained by an additional fifth planet. However, we stick to the initial conditions described in Read et al. (2018) for consistency. The outer edge of the disk follows from the ALMA observations by Booth et al. (2016).

5.2.1. Inner belt T able 5.1 : The orbital elements of 4 known planets HR 8799 e,d,c and b as in Go ´zdziewski & Migaszewski (2014, T able 1). In our simulations we adopted the nominal values from the table. Mp , a, e, i, Ω , ω and M correspond to the mass of the planet in Jupiter masses, the semi-major axis of the planet in A U , the eccentricity , the inclination in degrees, the longitude of the ascending node, the argument of pericenter and the mean anomaly at the epoch 1998.83 respectively . i is the inclination of coplanar orbits to the sky plane. i and Ω are assumed to be identical for all four planets; i is the best-fitting inclination of coplanar orbits to the sky plane. The stellar mass M˚ is 1.56M d . planet Mp (M jup ) a (A U) e i (deg) Ω (deg) ω (deg) M (deg) e 9 ˘ 2 15.4 ˘ 0.2 0.13 ˘ 0.03 25 ˘ 3 64 ˘ 3 46 ˘ 3 326 ˘ 5 d 9 ˘ 3 25.4 ˘ 0.3 0.12 ˘ 0.02 25 ˘ 3 64 ˘ 3 91 ˘ 3 58 ˘ 3 c 9 ˘ 3 39.4 ˘ 0.3 0.05 ˘ 0.02 25 ˘ 3 64 ˘ 3 151 ˘ 6 148 ˘ 6 b 7 ˘ 2 69.1 ˘ 0.2 0.020 ˘ 0.003 25 ˘ 3 64 ˘ 3 95 ˘ 10 321 ˘ 10

Eccentricities were set between 0 and 0.05 and inclinations between 00

and 2.860 _{(corresponding to 0.05 rad). The remaining, angular, orbital}

elements are randomly distributed between 00_{and 360}0 _{as for the inner}

belt. The simulations were performed forward in time for 70 Myr. The simulation’s time step was set to 0.48 yr in order to resolve the orbit of the innermost planet HR 8799 e, which has an orbital period of 48 years, and any close encounters that would occur between the planet and test particles.

5.3

S

:

ORBITAL STRUCTURE

,

The snapshot at 6 Myr shows that around that time the inner belt develops structure due to the interaction between the test particles and the planets, see Fig. 5.2. The interaction with the innermost planet HR 8799 e shapes the belt in a similar way Jupiter shapes our own Main Asteroid Belt. There are broad gaps at the locations of the mean motion resonances with the giant planets and there are many dynamically excited objects with large eccentricities and inclinations. At the end of the simulation, after 70 Myr, 928 test particles were discarded due to collisions with the star and 202,958 test particles were found to be ejected from the system. As shown in Table 5.2, 1,614 test particles collided with the innermost planet HR 8799 e, 92 with HR 8799 d, 44 with HR 8799 c, and 10 with HR 8799 b. As seen from Fig. 5.3, the number of impacts peaks prominently in the first 1 Myr. We attribute this to test particles that were initialised on highly unstable orbits. After the first „ 1 Myr, impacts continue at a roughly continuous rate, see Fig. 5.4; this will be referred to as ”steady state” in the following. The ”steady state” impact rates is what we are interested in for the purposes of this project.

The initial conditions of the inner belt simulations followed the example of Contro et al. (2016). As can be seen in our Figure 5.2 (see Fig. 3 in Contro et al., 2016), we reproduce the resulting structure of the inner belt from their simulations. At the end of the simulations there are almost no particles left beyond 8 AU. At the location of the 3:1 mean motion resonance with the innermost planet, at „ 7.4 AU, a broad gap is formed as well as a smaller gap at the location of the 4:1 mean motion resonance („ 6 AU). Unlike Contro et al. we resolve and analyse impacts between planets and test particles, see below.

5.3. SIMULATION RESULTS: ORBITAL STRUCTURE,IMPACT RATES

Figure 5.2: Time evolution of 650,000 test particles in the inner belt for a period of 70 Myr. All four planets are located outside of the plot. The innermost planet HR 8799 e has a semi-major axis of 15.4 AU.

Figure 5.3:Number of test particles originating from the inner belt that impacted with the planets, the star or exceeded a user-provided heliocentric distance, 1,000 AU, during 70 Myr of the simulations.

5.3. SIMULATION RESULTS: ORBITAL STRUCTURE,IMPACT RATES

Figure 5.4: The same as Fig. 5.3 but only after the first 1 Myr of the simulations, when the system reached steady state.

Table 5.2: Number of test particles that were discarded from the simulations of both belts due to the collisions with the star and four planets, and due to exceeding the maximum distance from the star.

simulation time belt ejection collision

star e d c b 0-70 Myr inner 202,958 928 1,614 92 44 10 outer 137,143 208 54 72 112 595 1-70 Myr inner 99,202 545 494 38 21 5 outer 35,205 17 4 9 6 18 5.3.2 Outer belt

In analogy with the inner belt, the structure of the outer belt is clearly visible by the time of the first snapshot at 6 Myr due to the interaction between the test particles and the planets as shown in Fig. 5.5. After 70 Myr, 208 test particles collided with the star and 137,143 test particles were ejected from the system. As seen in Table 5.2, the outermost planet HR 8799 b suffered from 595 impacts, HR 8799 c from 112, HR 8799 d from 72 and the innermost HR 8799 e from 54. Fig. 5.6 shows that most impacts occurred in the first 1 Myr. The majority of the impactors is produced by the test particles initialised on highly unstable orbits. Steady state is reached around 1 Myr. We are interested in those impacts that occur after steady state was reached, see Fig. 5.7. The structure of the outer belt that results in their simulations is the same as the one that we get in our simulations (compare to Fig. 2 in Read et al., 2018). The range of orbits within the initial inner edge of the outer belt, 69.1 AU, and 100 AU is depleted by the end of the simulations. At the location of the 2:1 mean motion resonance with the outermost planet, a broad gap is formed. Also the simulations produce a few HR 8799 b ”Trojans” orbiting at the same semi-major axis as the planet. Unlike Read et al. we resolve and analyse impacts between planets and test particles, see below.

5.3.3 Impact rates

The number of test particles impacting the planets from both belts are shown in Table 5.2. We only consider those impacts that occurred after the system reached steady state, 1-70 Myr. The innermost planet receives 7.2 and 0.06 impacts/Myr from the inner and the outer belts. Planet d receives 0.6 and 0.1 impacts/Myr, while planet c 0.3 and 0.09 impacts/Myr. The outermost planet receives 0.07 and 0.3 impacts/Myr.

5.3.2. Outer belt

Figure 5.5: The same as Fig. 5.2 but for the outer belt. 70 Myr evolution of 1,450,000 test particles. The outermost planet HR 8799 b has a semi-major axis of 69.1 AU.

Figure 5.6: Number of planet impactors originating from the outer belt after 10, 20, 30, ..., 70 Myr, respectively.

5.3.2. Outer belt

Figure 5.7: Number of planet impactors which happened after the first 1 Myr of the simulations, after the system reached steady state.

The total number of test particles, Ntp, in the inner belt is 544,659

and 1,347,075 in the outer belt. Note that these values represent the total number of test particles in either belt after the first 1 Myr when the system reached steady state and differ from the 650,000 test particles and 1,450,000 per inner and outer belts initialised at the start of the simulations.

5.4

Delivery rates

In Section 5.3 we have derived impact rates. Here, we use these to estimate the corresponding delivery rates of volatile (water and organics) and refractory (metals and silicates) material to the four planets.

The volatile delivery rate Rvoland the refractory delivery rate Rref r, for

each planet, can be expressed as (see Schwarz et al., 2018, Equation 3):

Rvol“ Mbeltˆ fvolˆ Nimp{Ntp{τsim, (5.2)

Rref r“ Mbeltˆ fref rˆ Nimp{Ntp{τsim, (5.3)

where Mbelt is the total mass of the belt, fvol and fref r are the mass

fraction of volatiles and refractories therein, Nimpis the number of impacts

on a planet from the corresponding belt, Ntpis the number of test particles

in the corresponding belt after the first 1 Myr of the simulation and τsim is

the simulation time. The simulation time τsim is 69 Myr and not 70 Myr

since we do not consider the impacts that happened in the first 1 Myr of the simulations. To estimate values of Mbelt, fvol and fref r for the inner

belt we use the Main Asteroid belt as a proxy and the Kuiper belt for the outer belt.

The values of Nimp, Ntp, τsim have been determined in Section 5.3.3.

In this section, we estimate Mbelt, fvol and fref r.

5.4.1 Belt masses

The total dust mass of either belt was determined by dust modelling based on infrared observations. According to Su et al. (2009) the total mass of the 1.5 ´ 4.5 µm sized dust grains in the inner belt is M_dustInner “ 1.1 ˆ 10´6_M

Cand the mass of the 10 ´ 1000 µm sized dust grains in the

5.4.2. Volatile content

model that would explain Herschel and ALMA observations of the outer belt. Their ”preferred” model predicts MplOuter “ 134 MCas the total mass

of the outer belt, assuming a size-frequency distribution of planetesimals up to a maximum diameter of 100 km. We adopt this value for our further calculations.

For the total planetesimal mass of the inner belt, however, there are no published estimates that we are aware of. We estimate the total belt mass (dust plus planetesimals) based on the dust mass determined by Su et al. (2009). In doing so, we assume a power law describing the differential size-frequency distribution npaq (diameter a) of a colliding steady state population of bodies:

npaq 9 a´q_{, (5.4)}

where q “ 3.5 (Dohnanyi, 1969; Bottke et al., 2015). The total mass of the inner belt for observed dust and for planetesimals can be calculated by integrating over the size distribution from the minimum to maximum dust sizes (from aminD “ 1.5 to amaxD “ 4.5 µm as observed by Su et al.

(2009)) and planetesimal sizes (aminD “ 1 m to amaxD “ 1000 km, based

on the size distribution of the Main Asteroid Belt):

mpă amaxq “ π 6 żamax amin npaq ρ a3da 9?a |amax amin. (5.5)

Normalising the total inner belt mass for asteroid size bodies by the total inner belt mass for dust particles gives:

MplInner MdustInner “ ? amaxA´?aminA ? amaxD´?aminD . (5.6)

In doing so, we found the total mass of the inner belt to be MplInner“

1.23 MC. For comparison, the estimated dust mass of the inner Solar

System is 7 ˆ 10´6_M

C(Nesvorn´y et al., 2011a) and the estimated mass

of the Main Asteroid Belt is 0.0004 MC(de Pater & Lissauer, 2015). The

planetesimal to dust mass ratio for the inner belt of the HR 8799 is 106 _and

103 _{for the Solar System.}

5.4.2 Volatile content

While it is reasonable to assume that the debris belts in HR 8799 contains some volatile material, no observational constraints are available. We

estimate the volatile content fvolof the inner and outer debris belt, basing

ourselves on knowledge from the Solar System.

Solar System asteroids belong to one of several taxonomic types. Only members of one such type, the so-called C-type asteroids, show appreciable amounts of volatiles. About 33% of all asteroids belong to this type (DeMeo & Carry, 2013). The water content of the C-type asteroids is « 10% by mass and their carbon content is « 2% by mass (National Research Council, 2007; Sephton et al., 2002; Sephton, 2014). Therefore, we adopt 0.33ˆp0.10`0.02q “ 0.04 as the fvolvalue for the inner belt of the HR 8799

system.

In contrast, the Kuiper Belt objects all are formed beyond the snow line which means that on average all those objects are expected to be volatile rich. However, the ice fraction measured in KBOs varies from 0 to 1 (Brown, 2012). Since the range of the volatile fraction is rather wide we adopted an average value of 50% as the fvolfor the HR 8799 outer belt.

The same value was adopted by Ciesla et al. (2015) and Schwarz et al. (2018) in their studies of volatile delivery.

After inserting all necessary values into Eq. 5.2 we calculate the volatile delivery rates, as shown in Table 5.3 from the inner and the outer belts to the four giant planets. The outer belt delivers an order of magnitude more volatiles to the planets despite the smaller total number of impacts. Especially for the outer belt our simulations yield few impacts which result in large Poisson noise, more than 50%, leading to large uncertainties.

5.4.3 Refractory content

Like for volatiles, we base our estimates of refractory-material content on our knowledge of the Solar System. In particular, we assume that any material not counted as volatile is refractory; in practice, the refractory component is likely to be dominated by silicates and metals. We therefore adopt a refractory content fref r of 0.96 for the inner belt and 0.5 for

the outer belt, respectively. The resulting delivery rates are presented in Table 5.3.

5.5

D

As Table 5.3 shows, volatiles and refractories are delivered from both belts to all four planets. The inner belt delivers to the planets 0.5 ˆ 10´7_M

C

of volatile material per Myr and 1.1 ˆ 10´5_M

C of refractory material

per Myr. The outer belt delivers 2.2 ˆ 10´5_M

C of volatiles per Myr and

2.2 ˆ 10´5_M

5.4.3. Refractory content T able 5.3 : V olatile delivery rates in Earth masses per Myr , M C /Myr , from the inner belt and the outer belt to the planets HR 8799 e, HR 8799 d, HR 8799 c, and HR 8799 b. belt e d c b volatiles inner 4 .10 ˘ 0 .02 ˆ 10 ´ 7 3 .3 ˘ 0 .7 ˆ 10 ´ 8 1 .7 ˘ 0 .5 ˆ 10 ´ 8 6 .5 ˘ 2 .9 ˆ 10 ´ 9 outer 2 .2 ˘ 1 .2 ˆ 10 ´ 6 5 .8 ˘ 2 .0 ˆ 10 ´ 6 2 .9 ˘ 1 .4 ˆ 10 ´ 6 1 .1 ˘ 0 .3 ˆ 10 ´ 5 refractories inner 9 .8 ˘ 0 .6 ˆ 10 ´ 6 7 .8 ˘ 1 .6 ˆ 10 ´ 7 4 .1 ˘ 1 .1 ˆ 10 ´ 7 1 .6 ˘ 0 .7 ˆ 10 ´ 7 outer 2 .2 ˘ 1 .2 ˆ 10 ´ 6 5 .8 ˘ 2 .0 ˆ 10 ´ 6 2 .9 ˘ 1 .4 ˆ 10 ´ 6 1 .1 ˘ 0 .3 ˆ 10 ´ 5

In terms of the impact rates the inner belt dominates the outer belt. For example, planet HR 8799 d experiences 0.6 impacts/Myr from the inner belt and 0.1 impacts/Myr from the outer belt. However, the outer belt is much more massive than the inner belt, two orders of magnitude, and its volatile fraction is an order of magnitude higher than for the inner belt. These differences result in the fact that the volatile delivery to the planets is dominated by the outer belt. On the other hand, the refractory fraction of the inner belt is almost twice as large as for the outer belt, which leads to similar refractory delivery rates from both belts.

Over the course of 69 Myr the four giant planets receive between 2 ˘ 1 ˆ 10´4_M

Cand 8 ˘ 2 ˆ 10´4MC of volatile material and between

2˘1ˆ10´4_M

Cand 8˘1ˆ10´4MCof refractory material. The uncertainty

is dominated by the Poisson noise in the simulated number of impacts and planetesimal masses of the belts. These total volatile and refractory fluxes are small compared to the total planet mass, which is 106_{´ 10}7_{times larger.}

Such an amount of volatile and/or refractory infall may be detectable in the upper layers of the planetary atmospheres. For example, gases with mixing ratios of „ 10´6 _{and even lower are often detectable, depending}

on species (de Pater & Lissauer, 2015).

Since the four giants HR 8799 e, d, c, b are beyond the snow line (and presumably formed there), we expect them to be born volatile-rich. Any future detection of volatiles would therefore not necessarily imply delivery through impacts. Silicates or other refractory material would be more diagnostic in this regard. Past observations of Jupiter after the impact of comet Shoemaker-Levy 9 and smaller objects may be used as a proxy for post impact enrichment observations of the giant planets in the HR 8799 system (Atreya et al., 1999; Fletcher et al., 2010).

The HR 8799 system may contain terrestrial planets, which presumably formed dry within the snow line. Volatile delivery from the belts may be of astrobiological importance for those. The same is true, probably, for possible terrestrial planets around other stars with asteroid-belt analogues. Given the lower mass of terrestrial planets (an Earth analogue would be about 2,800 less massive than HR 8799 e), the relative contribution of impactor material to the overall composition of the planet and its atmosphere could be much higher. Volatiles derived by impacts could be enough to explain an Earth-like atmosphere mass: Earth’s atmosphere contributes about 10´6_{of Earth’s total mass. We caution, however, that we}

did not (yet) model the impactor flux on terrestrial planets in the HR 8799 system.

The minor body collisions in the outer and inner belts of the HR 8799 system will produce dust, analogous to the zodiacal dust in the Solar system,

5.6. CONCLUSIONS

that may be observable with the upcoming HOSTS (Hunt for Observable Signatures of Terrestrial Systems) survey (Ertel et al., 2018b,a). Possible observation of the exozodiacal dust around HR 8799 may provide insights on the existence of terrestrial planets in the system and on the nature of the belts.

5.6

C

We performed numerical simulations of the inner and outer debris belts in the exoplanetary system HR 8799 to calculate for the first time delivery rates from the belts to the four planets. Delivery rates were separated into a volatile and a refractory component, respectively, where we base ourselves on Solar System knowledge.

• After the first 1 Myr the system reaches steady state. Also, in the first several Myr the HR 8799 belts develop orbital structure with gaps caused by the mean motion resonances with the planets (confirming previous work by Contro et al. (2016) and Read et al. (2018)). • All four planets experience impacts from the inner and outer belts.

The innermost planet HR 8799 e is affected the most by the objects from the inner belt. In turn, the outermost planet HR 8799 d experiences the most impacts from the outer belt.

• The outer belt delivers an order of magnitude more of the volatile material to the planets. The refractory delivery rates from the inner and the outer belt are similar, within the error bars.

• We expect the four giant planets to be born volatile-rich, so volatile delivery through impacts is probably insignificant in comparison. The enrichment in refractory material, however, may well be significant. JWST-MIRI observations targeting silicate features could be especially diagnostic and should be studied in detail.

A

We are thankful to Hanno Rein for valuable help with REBOUND, Jonathan

Horner for input on the inner belt, Matthew Read and Mark Wyatt for input

on the outer belt.

Simulations in this paper made use of the REBOUND code which can be downloaded freely at http://github.com/hannorein/rebound.

We would like to thank the Center for Information Technology of the University of Groningen for their support and for providing access to the Peregrine high performance computing cluster.